Recently, there has been much interest in developing quantitative phase imaging techniques for use in biological research, particularly at the cellular level (e.g., detecting sub-wavelength dynamics in biological samples). Techniques such as phase contrast and differential interference contrast microscopy have been used to image transparent samples by converting phase differences to intensity differences. These methods offer qualitative information about sample structure but suffer from a non-linear phase to amplitude conversion, thus they are unable to provide quantitative data. There has been much work in recent years to develop quantitative phase imaging techniques capable of detecting sub-wavelength dynamics in biological samples.
For instance, techniques such as phase contrast and differential interference contrast microscopy have been used to image transparent samples qualitatively by converting phase differences to intensity differences, but these methods suffer from a non-linear phase to amplitude conversion and thus do not directly provide quantitative data. In addition, phase shifting interferometry, digital holography, Fourier phase microscopy, and Hilbert phase microscopy are interferometric techniques that are capable of detecting nanometer scale features in biological specimens. These quantitative methods have applications in the realm of cellular imaging due to their high sensitivity and use of intrinsic contrast agents, but they lack the ability to obtain depth-resolved measurements from an optically thick sample.
The development of Fourier-domain optical coherence tomography (FDOCT), particularly spectrometer-based spectral-domain systems with no moving parts (spectral-domain OCT or SDOCT), has greatly enhanced the phase stability of optical coherence tomography (OCT) systems due to improvements to the system signal-to-noise ratio (SNR) over time domain systems. Common path implementations have given rise to a new class of functional, nanometer-scale sensitive quantitative phase microscopies termed spectral domain phase microscopy (SDPM) or spectral domain optical coherence phase microscopy (SDOCPM). Other implementations of OCT including swept-source OCT (SSOCT), optical frequency-domain imaging (OFDI) also depend in some applications on phase unwrapping.
In SDPM, phase information is obtained from Fourier processing as in standard SDOCT. The phase of a given depth sample represents sub-coherence length changes in the optical path length through the sample as a function of time or a lateral dimension and can be caused by changes to the refractive index, position of scattering objects, or both. SDPM is capable of producing depth-resolved phase maps measuring the motion of a dynamic sample throughout its volume. Using a common path geometry allows for cancellation of common mode noise, and such systems have experimental phase sensitivities as low as 53 picometers. SDPM has been used to study cytoplasmic streaming in Amoeba using Doppler flow, cytoskeletal rheology, and contractile motion of beating cardiomyocytes. All the aforementioned phase imaging modalities can suffer from phase wrapping artifacts.
The phase in the OCT signal is linearly related to the sample motion over time. The measured phase is limited, however, to a range of −π to +π. An artifact known as phase wrapping occurs when a change in phase between consecutive measurements is such that the total phase change falls outside this range and thus wraps to the opposite end of the range, yielding an ambiguous result. As SDPM operates in a reflection geometry, changes in a sample reflector's position greater than half of the source center wavelength will induce phase wrapping. In some cases, unwrapping the phase can be accomplished easily by adding or subtracting 2π to data points at jump discontinuities as long as the phase jump itself is no more than 2π. However, if a jump greater than 2π is present, this simple algorithm is no longer sufficient to correctly unwrap the phase.
Software implementations for phase unwrapping techniques have been used in SDPM, but they are often complex and computationally intensive. For example, one technique to resolve the 2π ambiguity in low coherence interferometery used a dispersion imbalance in the sample arm and polarization effects to simultaneously detect two interferograms from different lateral locations on a sample. This method required two spectrometer channels as well as additional polarization optics, which add complexity to the optical setup.
The use of two or three illuminating wavelengths to perform more robust phase unwrapping was first introduced in phase shifting interferometry and has since been applied in digital holography and phase imaging interference microscopy. The difference in the phase information obtained at two or more wavelengths can be cast in terms of an equivalent phase that would be obtained at a longer synthetic wavelength, Λ, which is a function of each of the imaging wavelengths. This method allows wrap-free measurements of changes in optical path length less than Λ/2, which can be significantly larger than any of the imaging wavelengths alone. A similar technique using a combination of low coherence and continuous wave sources was used to detect phase crossings in a Michelson interferometer allowing for phase wrap removal. These techniques require the use of multiple sources, which also complicate the optical setup. A similar technique in broadband interferometric confocal microscopy measured the group optical path delay through a sample by detecting relative phase changes between different wavelengths, allowing for measurement of the group refractive index while avoiding phase ambiguity.
Accordingly, in light of these difficulties, a need exists for improved methods, systems, and computer readable media for phase unwrapping of an OCT signal.